The grades on a math midterm at Springer are normally distributed with $\mu = 77$ and $\sigma = 5.0$. Omar earned a $90$ on the exam. Find the z-score for Omar's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Omar's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{90 - {77}}{{5.0}}} $ ${ z \approx 2.60}$ The z-score is $2.60$. In other words, Omar's score was $2.60$ standard deviations above the mean.